Rest of lecture 4 (Chapter 5: pg 115-121) Statistical Inferences

Draw inferences about the Inferential Statistics Sample Sample Population Sample Sample Draw inferences about the larger group

Sampling Error: variability among samples due to chance vs population Or true differences? Are just due to sampling error? Probability….. Error…misleading…not a mistake

Are inferences valid…Best we can do is to calculate probability data Are inferences valid…Best we can do is to calculate probability about inferences

Inferential Statistics: uses sample data to evaluate the credibility of a hypothesis about a population NULL Hypothesis: NULL (nullus - latin): “not any”  no differences between means H0 : m1 = m2 “H- Naught” Always testing the null hypothesis

Inferential statistics: uses sample data to evaluate the credibility of a hypothesis about a population Hypothesis: Scientific or alternative hypothesis Predicts that there are differences between the groups H1 : m1 = m2

Inferential Statistics When making comparisons btw 2 sample means there are 2 possibilities Null hypothesis is false Null hypothesis is true Reject the Null hypothesis Not reject the Null Hypothesis

ALPHA the probability of making a type I error  depends on the criterion you use to accept or reject the null hypothesis = significance level (smaller you make alpha, the less likely you are to commit error) 0.05 (5 chances in 100 that the difference observed was really due to sampling error – 5% of the time a type I error will occur) Alpha (a) Difference observed is really just sampling error The prob. of type one error

When we do statistical analysis… if alpha (p value- significance level) greater than 0.05 WE ACCEPT THE NULL HYPOTHESIS is equal to or less that 0.05 we REJECT THE NULL (difference btw means)

BETA Probability of making type II error  occurs when we fail to reject the Null when we should have Beta (b) Difference observed is real Failed to reject the Null POWER: ability to reduce type II error

Effect Size: measure of the size of the difference POWER: ability to reduce type II error (1-Beta) – Power Analysis The power to find an effect if an effect is present Increase our n 2. Decrease variability 3. More precise measurements Effect Size: measure of the size of the difference between means attributed to the treatment

Significance testing: Practical vs statistical significance Inferential statistics Significance testing: Practical vs statistical significance

T-test: when experiments include only 2 groups Inferential statistics Used for Testing for Mean Differences T-test: when experiments include only 2 groups Independent b. Correlated i. Within-subjects ii. Matched Based on the t statistic (critical values) based on df & alpha level

Analysis of Variance (ANOVA): used when Inferential statistics Used for Testing for Mean Differences Analysis of Variance (ANOVA): used when comparing more than 2 groups 1. Between Subjects 2. Within Subjects – repeated measures Based on the f statistic (critical values) based on df & alpha level More than one IV = factorial (iv=factors) Only one IV=one-way anova

Allows for statistical averaging of results Inferential statistics Meta-Analysis: Allows for statistical averaging of results From independent studies of the same phenomenon